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(real_minus_real_is_real application-judgement "real" reals nil)
(real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(real_times_real_is_real application-judgement "real" reals nil)
(real_plus_real_is_real application-judgement "real" reals nil)
(posreal_times_posreal_is_posreal application-judgement "posreal"
real_types nil)
(dot_scal_left formula-decl nil vectors_2D "vectors/")
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(boolean nonempty-type-decl nil booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
(real nonempty-type-from-decl nil reals nil)
(Vector type-eq-decl nil vectors_2D "vectors/")
(/= const-decl "boolean" notequal nil)
(zero const-decl "Vector" vectors_2D "vectors/")
(Nz_vect2 type-eq-decl nil vectors_2D "vectors/")
(Vect2 type-eq-decl nil vectors_2D_def "vectors/")
(number nonempty-type-decl nil numbers nil)
(number_field_pred const-decl "[number -> boolean]" number_fields
nil)
(number_field nonempty-type-from-decl nil number_fields nil)
(real_pred const-decl "[number_field -> boolean]" reals nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(gs_only? const-decl "bool" definitions nil)
(= const-decl "[T, T -> boolean]" equalities nil)
(* const-decl "real" vectors_2D "vectors/")
(- const-decl "Vector" vectors_2D "vectors/")
(gs_only_dot const-decl
"{nvo | nvo /= zero => gs_only?(vo)(nvo) AND u * (nvo - vi) = j}"
gs_only nil)
(* const-decl "Vector" vectors_2D "vectors/")
(>= const-decl "bool" reals nil)
(nonneg_real nonempty-type-eq-decl nil real_types nil)
(> const-decl "bool" reals nil)
(posreal nonempty-type-eq-decl nil real_types nil)
(+ const-decl "Vector" vectors_2D "vectors/")
(D formal-const-decl "posreal" gs_only nil)
(Delta const-decl "real" horizontal nil)
(rational_pred const-decl "[real -> boolean]" rationals nil)
(rational nonempty-type-from-decl nil rationals nil)
(integer_pred const-decl "[rational -> boolean]" integers nil)
(int nonempty-type-eq-decl nil integers nil)
(nzint nonempty-type-eq-decl nil integers nil)
(OR const-decl "[bool, bool -> bool]" booleans nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(- const-decl "[numfield -> numfield]" number_fields nil)
(Sign type-eq-decl nil sign "reals/")
(Theta_D const-decl "real" horizontal nil)
(- const-decl "[numfield, numfield -> numfield]" number_fields nil)
(sq const-decl "nonneg_real" sq "reals/"))
nil)))
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